23.1.340 problem 326

Internal problem ID [4947]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 326
Date solved : Tuesday, September 30, 2025 at 09:03:52 AM
CAS classification : [_linear]

\begin{align*} \left (x -a \right ) \left (x -b \right ) y^{\prime }&=\left (x -a \right ) \left (x -b \right )+\left (2 x -a -b \right ) y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 44

ode:=(x-a)*(x-b)*diff(y(x),x) = (x-a)*(x-b)+(2*x-a-b)*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-x +b \right ) \left (-x +a \right ) \left (\ln \left (x -a \right )-\ln \left (x -b \right )+c_1 \left (a -b \right )\right )}{a -b} \]

✓ Mathematica. Time used: 0.082 (sec). Leaf size: 85

ode=(x-a)*(x-b)*D[y[x],x]==(x-a)*(x-b)+(2*x-a-b)y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \exp \left (\int _1^x\frac {a+b-2 K[1]}{(a-K[1]) (K[1]-b)}dK[1]\right ) \left (\int _1^x\exp \left (-\int _1^{K[2]}\frac {a+b-2 K[1]}{(a-K[1]) (K[1]-b)}dK[1]\right )dK[2]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.826 (sec). Leaf size: 114

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq((-a + x)*(-b + x)*Derivative(y(x), x) - (-a + x)*(-b + x) - (-a - b + 2*x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} a^{2} b - C_{1} a^{2} x - C_{1} a b^{2} + C_{1} a x^{2} + C_{1} b^{2} x - C_{1} b x^{2} + a b \log {\left (- a + x \right )} - a b \log {\left (- b + x \right )} - a x \log {\left (- a + x \right )} + a x \log {\left (- b + x \right )} - b x \log {\left (- a + x \right )} + b x \log {\left (- b + x \right )} + x^{2} \log {\left (- a + x \right )} - x^{2} \log {\left (- b + x \right )}}{a - b} \]